# Finding the max frequency of a driven oscillator

• I
So I've derived the equation for the amplitude of a driven oscillator as:

$\huge A=\frac{F}{m\sqrt{(\omega_{0}^{2}-\omega_{d}^{2})^{2}+4\gamma^{2}\omega_{d}^{2}}}$

Which is what my lecturer has written. Then taking the derivative and setting it to 0 to get the turning point. He makes this leap:

https://imgur.com/a/gE7Y0Di

How does he do that? I can't do it.

Also an auxiliary question. I was watching Walter Lewin on this here .
And he uses

$\huge {\gamma}=\frac{b}{m}$

Whereas I've been taught:

$\huge {\gamma}=\frac{b}{2m}$

Where ϒ is the damping coefficient. Which is correct?